Question: $f(t) = -6t^{2}-3t+3(g(t))$ $g(x) = 5x^{2}-6x$ $ f(g(2)) = {?} $
First, let's solve for the value of the inner function, $g(2)$ . Then we'll know what to plug into the outer function. $g(2) = 5(2^{2})+(-6)(2)$ $g(2) = 8$ Now we know that $g(2) = 8$ . Let's solve for $f(g(2))$ , which is $f(8)$ $f(8) = -6(8^{2})+(-3)(8)+3(g(8))$ To solve for the value of $f$ , we need to solve for the value of $g(8)$ $g(8) = 5(8^{2})+(-6)(8)$ $g(8) = 272$ That means $f(8) = -6(8^{2})+(-3)(8)+(3)(272)$ $f(8) = 408$